Isoelastic utility

There is substantial debate in the economics and finance literature with respect to the true value of \eta. While extremely high values of \eta (of up to 50 in some models) are needed to explain the behavior of asset prices, most experiments document behavior that is more consistent with values of \eta only slightly greater than 1. For example, Groom and Maddison (2019) estimated the value of \eta to be 1.5 in the United Kingdom, while Evans (2005) estimated its value to be around 1.4 in 20 OECD countries. The utility of income can also be estimated using subjective well-being surveys. Using six national and international such surveys, Layard et al. (2008) found values between 1.19 an 1.34 with a combined estimate of 1.26. == Risk aversion features ==

This utility function has the feature of constant relative risk aversion. Mathematically this means that -c \cdot u''(c)/u'(c) is a constant, specifically In theoretical models this often has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth. == Special cases ==

• \eta=0: this corresponds to risk neutrality, because utility is linear in c. • \eta=1: by virtue of l'Hôpital's rule, the limit of u(c) is \ln c as \eta goes to 1: ::\lim_{\eta\rightarrow1}\frac{c^{1-\eta}-1}{1-\eta}=\ln(c) :which justifies the convention of using the limiting value u(c) = ln c when \eta=1. • \eta → \infty: this is the case of infinite risk aversion. == See also ==